Integral Conservation Physics-Informed Neural Networks with different network architectures for patient-specific aortic flow simulations

Abstract

The numerical simulation of blood flow in the patient-specific thoracic aorta not only accurately reproduces personalized hemodynamic characteristics but also provides robust data support for the diagnosis and treatment of vascular diseases. This study advances the numerical simulation of blood flow in patient-specific thoracic aortas by extending our previously developed Integral Conservation Physics-Informed Neural Networks (ICPINNs) framework (Liu et al., 2025) from steady-state to transient flow problems. The ICPINNs method leverages the integral conservation form of the nonlinear Navier–Stokes equations, incorporating residual terms derived from both governing equations and training data, with Monte Carlo integration employed for integrals. We address two main classes of aortas: (1) unsupervised learning for anomalous branching of the aorta, and (2) integration of sparse velocity measurements for geometrically complex healthy and pathological full thoracic aortas. Furthermore, we conduct the first systematic comparison of different neural network architectures for real-world transient aortic flows, assessing their computational efficiency and accuracy against conventional numerical solutions. Numerical results demonstrate that fully-connected neural networks within the ICPINNs framework achieves optimal performance for healthy aortas, while more sophisticated architectures such as the Deep Galerkin Method prove superior for modeling complex pathologies like Marfan syndrome-associated aneurysms, despite increased computational costs. This work represents an important step toward personalized hemodynamic modeling, offering clinically relevant insights that could enhance diagnostic precision and therapeutic planning for cardiovascular diseases.